Adaptive nonlinear dynamical initialization

An adaptive nonlinear initialization scheme is presented that provides improvements over linear relaxation methods for approaching the target state while minimizing discontinuities in dynamical models. The method adds an adaptive nonlinear forcing term to the model equations that is a function of the difference between the model field and its target value. A new feature is that the amplitude of the forcing is nonlinearly adapted to the size of the difference, allowing for stronger relaxation where differences are large and weaker relaxation where differences are small. We find that the function leads to more optimal introduction of new information by working hardest at the beginning of the initialization period while converging toward a steady condition for the majority of the domain at the end of the initialization period. Experiments with a limited area ocean model, with different dynamical regimes, show that the adaptive scheme leads to less shock than standard linear approaches and permits the model to converge to a state away from the target field if the target is not a priori dynamically balanced. Results indicate that the method has the potential to lower forecast error. This suggests that it will have a broad range of applications in dynamical prediction systems.